mensuration area volumes Model Questions & Answers, Practice Test for ibps so prelims 2023

Answer: (a)

Let the radii and slant height of two right circular cones are $r_1 , l_1 and r_2 , l_2$ , respectively.

∴ Ratio of their curved surface areas

= ${πr_1l_1}/{πr_2l_2} = l_1/l_2 (∵ r_1 = r_2)$

= $3/2$ = 3 : 2

Answer: (b)

Diameter of a sphere, d = 6 cm

∴ Radius of a sphere, r = $d/2 = 6/2$ = 3 cm

Let the radius of wire be R cm.

Also, given the length of wire, H = 36 m = 3600 cm

According to question

Volume of sphere = Volume of wire

⇒ $4/3 π r^3 = π R^2 H$

⇒ $4/3 × (3)^3 = R^2 × 3600$

⇒ $R^2 = {4 × 3^2}/{3600} = {(6)^2}/{(60)^2}$

∴ R = $6/{60} = 1/{10}$ = 0.1 cm

Answer: (d)

Side of equilateral Δ = l

Then,

In radius of circle = $l/{2√3}$

which is diagonal of the square inscribe in the circle

Let, side of square = x

Then,

$x^2 + x^2 = (l/√3)^2$

$2x^2 = l^2/3$

Area of square, $x^2 = l^2/6$

Answer: (c)

Let the side of cube = a

According to question

Height = a, radius = $a/2$

r = $a/2$ , h = a

Radius of sphere (R) = $a/2$

∴ Volume of cone (C)

= $1/3 πr^2h = 1/3 π(a/2)^2 a ={πa^3}/{12}$ ...(i)

Volume of sphere (S) = $4/3 πR^3 = 4/3 π(a/2)^3$

= ${πa^3}/6$ ...(ii)

On solving eqs. (i) and (ii),

S = 2C

Answer: (d)

1 kg = 1000 $cm^3$

2700 = k.$2^3$

k = ${2700}/8$

6300 = k. $r^3$

$r^3 = {6300}/{k} = {6300}/{2700} = {8/3},$

$r^3 = {56}/{3}$ = , r = 2.6 cm